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%I #29 Sep 08 2022 08:45:08
%S 0,1,2,19,68,421,1862,10039,48008,246601,1213322,6125659,30451148,
%T 152787181,762341582,3816490879,19068105488,95383574161,476788730642,
%U 2384331073699,11920493107028,59605952319541,298019301244502
%N a(n) = 2*a(n-1)+15*a(n-2) with n>0, a(0)=0, a(1)=1.
%D F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
%H Vincenzo Librandi, <a href="/A079773/b079773.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,15)
%F G.f.: x/((1+3*x)*(1-5*x)).
%F a(n) = (5^n-(-3)^n)/8.
%F a(n) = sum(k=1..n, binomial(n, 2*k-1)*4^(2*(k-1))).
%F E.g.f.: exp(x)*sinh(4*x)/4. - _Paul Barry_, Jul 09 2003
%F a(n+1) = Sum_{k = 0..n} A238801(n,k)*4^k. - _Philippe Deléham_, Mar 07 2014
%t Join[{a=0,b=1},Table[c=2*b+15*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t CoefficientList[Series[x / ((1 + 3 x) (1 - 5 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%o (Sage) [lucas_number1(n,2,-15) for n in range(0, 23)] # _Zerinvary Lajos_, Apr 22 2009
%o (Magma) [(5^n-(-3)^n)/8: n in [0..25]]; // _Vincenzo Librandi_, Aug 05 2013
%Y Cf. A051958, A015441.
%K nonn,easy
%O 0,3
%A _Paul Barry_, Feb 20 2003
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